
Given an ELLC vector field \(f:\mathcal {Z}\subset \mathcal {R}^{n_z} \rightarrow \mathbb {R}^{n_x}\) , construct a tractable family of mixed-monotone remainder-form (i.e., additive) decomposition functions for \(f(\cdot )\) .

Derive lower and upper bounds for the tightness (quantified via (REF )) of the family of remainder-form decomposition functions obtained in 1.REF .

Find the tightest decomposition function(s) among the family of remainder-form decomposition functions
obtained in 1.REF  and compare them with the decomposition function in [1]} (cf. Proposition REF ), and natural, centered and mixed-centered natural inclusions (cf. Proposition REF ).


